Block code: Difference between revisions

Revision as of 23:57, 24 May 2019

Revision as of 00:00, 25 May 2019

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The data stream to be encoded is modeled as a [[string (computer science)|string]] over some '''alphabet''' <math>\Sigma</math>. The size <math>|\Sigma|</math> of the alphabet is often written as <math>q</math>. If <math>q=2</math>, then the block code is called a ''binary'' block code. In many applications it is useful to consider <math>q</math> to be a [[prime power]], and to identify <math>\Sigma</math> with the [[finite field]] <math>\mathbb F_q</math>.

=== The message length ''k'' ===

<math>k</math> in Morse code is ?????

Messages are elements <math>m</math> of <math>\Sigma^k</math>, that is, strings of length <math>k</math>.

Hence the number <math>k</math> is called the '''message length''' or '''dimension''' of a block code.

=== The block length ''n'' ===